The following presentation was given as part of the COMPUTE seminar series and is available as video via YouTube.

Speaker: Daniel Tamayo (Princeton)

Title: Generalization and confidence intervals for machine learning models in the Sciences: Application to predicting the long-term stability of planetary systems

Abstract:
Several hundred multi-planet systems have been discovered around stars other than our own. These are indirect and challenging detections at the limit of observational capabilities, which often leave many important physical parameters uncertain, notably masses and orbital eccentricities. Interestingly, many of these multi-planet systems are in compact orbital configurations, which in principle allow one to rule out the wide ranges of parameter space that quickly lead to dynamical chaos and planetary collisions. Unfortunately, direct evaluation of stability through numerical integration is computationally prohibitive due to the long dynamical ages of these worlds.

This unsolved problem of determining the long-term stability of given orbital configurations has a rich history, partially motivating the discovery of dynamical chaos and driving the development of non-linear dynamics. I will present our latest work combining our partial understanding of the dynamics in these systems with machine learning methods to significantly improve on previous efforts and computationally open up of the stability constrained characterization of exoplanet systems. Our complementary work on this problem highlights the tradeoffs between manual feature engineering and data-driven features discovered through deep learning for complex problems in the sciences. Finally, I will discuss our latest efforts to go beyond simple point-estimates to training models that additionally provide confidence intervals using Bayesian Neural Networks and the newly developed Multi-SWAG algorithm (Wilson & Izmailov 2020).